///////////////////////////////////////////////////////////////////////////////////
/// OpenGL Mathematics (glm.g-truc.net)
///
/// Copyright (c) 2005 - 2015 G-Truc Creation (www.g-truc.net)
/// Permission is hereby granted, free of charge, to any person obtaining a copy
/// of this software and associated documentation files (the "Software"), to deal
/// in the Software without restriction, including without limitation the rights
/// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
/// copies of the Software, and to permit persons to whom the Software is
/// furnished to do so, subject to the following conditions:
/// 
/// The above copyright notice and this permission notice shall be included in
/// all copies or substantial portions of the Software.
/// 
/// Restrictions:
///		By making use of the Software for military purposes, you choose to make
///		a Bunny unhappy.
/// 
/// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
/// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
/// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
/// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
/// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
/// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
/// THE SOFTWARE.
///
/// @ref core
/// @file glm/detail/func_matrix.inl
/// @date 2008-03-08 / 2011-06-15
/// @author Christophe Riccio
///////////////////////////////////////////////////////////////////////////////////

#include "../geometric.hpp"
#include <limits>

namespace glm {
    namespace detail {
        template<template<class, precision> class matType, typename T, precision P>
        struct compute_transpose {
        };

        template<typename T, precision P>
        struct compute_transpose<tmat2x2, T, P> {
            GLM_FUNC_QUALIFIER static tmat2x2<T, P> call(tmat2x2<T, P> const &m) {
                tmat2x2<T, P> result(uninitialize);
                result[0][0] = m[0][0];
                result[0][1] = m[1][0];
                result[1][0] = m[0][1];
                result[1][1] = m[1][1];
                return result;
            }
        };

        template<typename T, precision P>
        struct compute_transpose<tmat2x3, T, P> {
            GLM_FUNC_QUALIFIER static tmat3x2<T, P> call(tmat2x3<T, P> const &m) {
                tmat3x2<T, P> result(uninitialize);
                result[0][0] = m[0][0];
                result[0][1] = m[1][0];
                result[1][0] = m[0][1];
                result[1][1] = m[1][1];
                result[2][0] = m[0][2];
                result[2][1] = m[1][2];
                return result;
            }
        };

        template<typename T, precision P>
        struct compute_transpose<tmat2x4, T, P> {
            GLM_FUNC_QUALIFIER static tmat4x2<T, P> call(tmat2x4<T, P> const &m) {
                tmat4x2<T, P> result(uninitialize);
                result[0][0] = m[0][0];
                result[0][1] = m[1][0];
                result[1][0] = m[0][1];
                result[1][1] = m[1][1];
                result[2][0] = m[0][2];
                result[2][1] = m[1][2];
                result[3][0] = m[0][3];
                result[3][1] = m[1][3];
                return result;
            }
        };

        template<typename T, precision P>
        struct compute_transpose<tmat3x2, T, P> {
            GLM_FUNC_QUALIFIER static tmat2x3<T, P> call(tmat3x2<T, P> const &m) {
                tmat2x3<T, P> result(uninitialize);
                result[0][0] = m[0][0];
                result[0][1] = m[1][0];
                result[0][2] = m[2][0];
                result[1][0] = m[0][1];
                result[1][1] = m[1][1];
                result[1][2] = m[2][1];
                return result;
            }
        };

        template<typename T, precision P>
        struct compute_transpose<tmat3x3, T, P> {
            GLM_FUNC_QUALIFIER static tmat3x3<T, P> call(tmat3x3<T, P> const &m) {
                tmat3x3<T, P> result(uninitialize);
                result[0][0] = m[0][0];
                result[0][1] = m[1][0];
                result[0][2] = m[2][0];

                result[1][0] = m[0][1];
                result[1][1] = m[1][1];
                result[1][2] = m[2][1];

                result[2][0] = m[0][2];
                result[2][1] = m[1][2];
                result[2][2] = m[2][2];
                return result;
            }
        };

        template<typename T, precision P>
        struct compute_transpose<tmat3x4, T, P> {
            GLM_FUNC_QUALIFIER static tmat4x3<T, P> call(tmat3x4<T, P> const &m) {
                tmat4x3<T, P> result(uninitialize);
                result[0][0] = m[0][0];
                result[0][1] = m[1][0];
                result[0][2] = m[2][0];
                result[1][0] = m[0][1];
                result[1][1] = m[1][1];
                result[1][2] = m[2][1];
                result[2][0] = m[0][2];
                result[2][1] = m[1][2];
                result[2][2] = m[2][2];
                result[3][0] = m[0][3];
                result[3][1] = m[1][3];
                result[3][2] = m[2][3];
                return result;
            }
        };

        template<typename T, precision P>
        struct compute_transpose<tmat4x2, T, P> {
            GLM_FUNC_QUALIFIER static tmat2x4<T, P> call(tmat4x2<T, P> const &m) {
                tmat2x4<T, P> result(uninitialize);
                result[0][0] = m[0][0];
                result[0][1] = m[1][0];
                result[0][2] = m[2][0];
                result[0][3] = m[3][0];
                result[1][0] = m[0][1];
                result[1][1] = m[1][1];
                result[1][2] = m[2][1];
                result[1][3] = m[3][1];
                return result;
            }
        };

        template<typename T, precision P>
        struct compute_transpose<tmat4x3, T, P> {
            GLM_FUNC_QUALIFIER static tmat3x4<T, P> call(tmat4x3<T, P> const &m) {
                tmat3x4<T, P> result(uninitialize);
                result[0][0] = m[0][0];
                result[0][1] = m[1][0];
                result[0][2] = m[2][0];
                result[0][3] = m[3][0];
                result[1][0] = m[0][1];
                result[1][1] = m[1][1];
                result[1][2] = m[2][1];
                result[1][3] = m[3][1];
                result[2][0] = m[0][2];
                result[2][1] = m[1][2];
                result[2][2] = m[2][2];
                result[2][3] = m[3][2];
                return result;
            }
        };

        template<typename T, precision P>
        struct compute_transpose<tmat4x4, T, P> {
            GLM_FUNC_QUALIFIER static tmat4x4<T, P> call(tmat4x4<T, P> const &m) {
                tmat4x4<T, P> result(uninitialize);
                result[0][0] = m[0][0];
                result[0][1] = m[1][0];
                result[0][2] = m[2][0];
                result[0][3] = m[3][0];

                result[1][0] = m[0][1];
                result[1][1] = m[1][1];
                result[1][2] = m[2][1];
                result[1][3] = m[3][1];

                result[2][0] = m[0][2];
                result[2][1] = m[1][2];
                result[2][2] = m[2][2];
                result[2][3] = m[3][2];

                result[3][0] = m[0][3];
                result[3][1] = m[1][3];
                result[3][2] = m[2][3];
                result[3][3] = m[3][3];
                return result;
            }
        };

        template<template<class, precision> class matType, typename T, precision P>
        struct compute_determinant {
        };

        template<typename T, precision P>
        struct compute_determinant<tmat2x2, T, P> {
            GLM_FUNC_QUALIFIER static T call(tmat2x2<T, P> const &m) {
                return m[0][0] * m[1][1] - m[1][0] * m[0][1];
            }
        };

        template<typename T, precision P>
        struct compute_determinant<tmat3x3, T, P> {
            GLM_FUNC_QUALIFIER static T call(tmat3x3<T, P> const &m) {
                return
                        +m[0][0] * (m[1][1] * m[2][2] - m[2][1] * m[1][2])
                        - m[1][0] * (m[0][1] * m[2][2] - m[2][1] * m[0][2])
                        + m[2][0] * (m[0][1] * m[1][2] - m[1][1] * m[0][2]);
            }
        };

        template<typename T, precision P>
        struct compute_determinant<tmat4x4, T, P> {
            GLM_FUNC_QUALIFIER static T call(tmat4x4<T, P> const &m) {
                T SubFactor00 = m[2][2] * m[3][3] - m[3][2] * m[2][3];
                T SubFactor01 = m[2][1] * m[3][3] - m[3][1] * m[2][3];
                T SubFactor02 = m[2][1] * m[3][2] - m[3][1] * m[2][2];
                T SubFactor03 = m[2][0] * m[3][3] - m[3][0] * m[2][3];
                T SubFactor04 = m[2][0] * m[3][2] - m[3][0] * m[2][2];
                T SubFactor05 = m[2][0] * m[3][1] - m[3][0] * m[2][1];

                tvec4<T, P> DetCof(
                        +(m[1][1] * SubFactor00 - m[1][2] * SubFactor01 + m[1][3] * SubFactor02),
                        -(m[1][0] * SubFactor00 - m[1][2] * SubFactor03 + m[1][3] * SubFactor04),
                        +(m[1][0] * SubFactor01 - m[1][1] * SubFactor03 + m[1][3] * SubFactor05),
                        -(m[1][0] * SubFactor02 - m[1][1] * SubFactor04 + m[1][2] * SubFactor05));

                return
                        m[0][0] * DetCof[0] + m[0][1] * DetCof[1] +
                        m[0][2] * DetCof[2] + m[0][3] * DetCof[3];
            }
        };
    }//namespace detail

    template<typename T, precision P, template<typename, precision> class matType>
    GLM_FUNC_QUALIFIER matType<T, P>
    matrixCompMult(matType<T, P> const &x, matType<T, P> const &y) {
        GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559,
                          "'matrixCompMult' only accept floating-point inputs");

        matType<T, P> result(uninitialize);
        for (detail::component_count_t i = 0; i < detail::component_count(result); ++i)
            result[i] = x[i] * y[i];
        return result;
    }

    template<typename T, precision P, template<typename, precision> class vecTypeA,
            template<typename, precision> class vecTypeB>
    GLM_FUNC_QUALIFIER typename detail::outerProduct_trait<T, P, vecTypeA, vecTypeB>::type
    outerProduct(vecTypeA<T, P> const &c, vecTypeB<T, P> const &r) {
        GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559,
                          "'outerProduct' only accept floating-point inputs");

        typename detail::outerProduct_trait<T, P, vecTypeA, vecTypeB>::type m(uninitialize);
        for (detail::component_count_t i = 0; i < detail::component_count(m); ++i)
            m[i] = c * r[i];
        return m;
    }

    template<typename T, precision P, template<typename, precision> class matType>
    GLM_FUNC_QUALIFIER typename matType<T, P>::transpose_type transpose(matType<T, P> const &m) {
        GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559,
                          "'transpose' only accept floating-point inputs");
        return detail::compute_transpose<matType, T, P>::call(m);
    }

    template<typename T, precision P, template<typename, precision> class matType>
    GLM_FUNC_QUALIFIER T determinant(matType<T, P> const &m) {
        GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559,
                          "'determinant' only accept floating-point inputs");
        return detail::compute_determinant<matType, T, P>::call(m);
    }

    template<typename T, precision P, template<typename, precision> class matType>
    GLM_FUNC_QUALIFIER matType<T, P> inverse(matType<T, P> const &m) {
        GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559,
                          "'inverse' only accept floating-point inputs");
        return detail::compute_inverse(m);
    }

}//namespace glm
